Is it “any repetitive action”? Or, has been claimed elsewhere (per FN 348 of this book), is “quaevis” an imperative form of the verb “quaero”, so the translation would be “To seek a repeat performance (or action)”?

Various suggestions have been offered as to the formation. Need was evidently felt of a noun of condition or quality from idem to express the notion of ‘sameness’, side by side with those of ‘likeness’ and ‘oneness’ expressed by similitās and ūnitās: hence the form of the suffix. But idem had no combining stem. Some have thought that ident(i)- was taken from the L. adv. identidem ‘over and over again, repeatedly’, connexion with which appears to be suggested by Du Cange's explanation of identitās as ‘quævis actio repetita’. Meyer-Lübke suggests that in the formation there was present some association between idem and id ens ‘that being’, whence identitās like entitās. But assimilation to entitās may have been merely to avoid the solecism of *idemitās or *idemtās. However originated, ident(i)- became the combining stem of idem, and the series ūnitās, ūnicus, ūnificus, ūnificāre, was paralleled by identitās, identicus, identificus, identificāre: see identic, identific, identify above.]

to OED 3rd:

identity, n. Pronunciation: Brit./ʌɪˈdɛntᵻti/ , U.S. /aɪˈdɛn(t)ədi/ Forms: 15 idemptitie, 15 ydemptyte, 15–16 identitie, 15– identity, 16 idemptity. Etymology: < Middle French identité, ydemtité, ydemptité, ydentité (French identité) quality or condition of being the same (a1310; 1756 in sense ‘individuality, personality’, 1801 in sense ‘distinct impression of a single person or thing presented to or perceived by others’) and its etymon post-classical Latin identitat-, identitas quality of being the same (4th cent.), condition or fact that a person or thing is itself and not something else (8th cent. in a British source), fact of being the same (from 12th cent. in British sources), continual sameness, lack of variety, monotony (from 12th cent. in British sources; 14th cent. in a continental source) < classical Latin idem same (see idem n.) + -tās (see -ty suffix1) [sameness], after post-classical Latin essentitas ‘being’ (4th cent.); the Latin word was formed to provide a translation equivalent for ancient Greek ταὐτότης identity.

The two OED explanations aren't completely inconsistent. The Latin word identitas itself is difficult to explain on the basis of the normal principles of Latin word formation. The 3rd ed. OED definition seems closer to the mark-- formed on the basis of idem, which is also the basis for identidem, rather than on the basis of identidem, as a calque of a Greek philosophical term first occurring apparently in Aristotle.

Perhaps the second ed. is correct that the first instance of identitas in the surviving body of Latin literature shows up in the late, post-classical Latin authors Victorinus or Martianus Capella. Of course, it may well have been used earlier in works that haven't survived. Du Cange's derivation from i]identidem[/i], and his definition, quævis actio repetita, seem suspect.